It is sometimes desirable to have circuits capable of selectively filtering one frequency or range of frequencies out of a mix of different frequencies in a circuit. A circuit designed to perform this frequency selection is called a filter circuit, or simply a filter. Filters are used in a vast number of practical applications.
For example, a common need for filter circuits is in high-performance stereo systems, where certain ranges of audio frequencies need to be amplified or suppressed for best sound quality and power efficiency. For example, equalizers allow the amplitudes of several frequency ranges to be adjusted to suit the listener's taste and acoustic properties of the listening area. In contrast, crossover networks block certain ranges of frequencies from reaching speakers. Both equalizers and crossover networks are examples of filters, designed to accomplish filtering of certain frequencies.
Another practical application of filter circuits is in the “conditioning” of non-sinusoidal voltage waveforms in power circuits. Some electronic devices are sensitive to the presence of harmonics in the power supply voltage, and so require power conditioning for proper operation. If a distorted sine-wave voltage behaves like a series of harmonic waveforms added to the fundamental frequency, then it should be possible to construct a filter circuit that only allows the fundamental waveform frequency to pass through, blocking all (higher-frequency) harmonics.
Frequency-selective or filter circuits pass to the output only those input signals that are in a desired range of frequencies (called pass band). The amplitude of signals outside this range of frequencies (called stop band) is reduced (ideally reduced to zero). Typically, in these circuits, the input and output currents are kept to a small value and as such, the current transfer function is less important parameter than the voltage transfer function in the frequency domain.
FIG. 1 shows a conventional 1st order passive low pass filter 100 which includes a resistor 101 and a capacitor 102 connected in series so that they can accept the same current. The input terminal 110 is connected across the whole circuit whereas the output terminal 120 is connected across the positive capacitor. The filter 100 is simple in implementation, but does not provide a gain greater than 0 dB and/or a rapid power roll off with a value more than 20 dB/decade around and beyond a cutoff frequency.
FIG. 2A shows an exemplar Gain vs Frequency curve 200 for a first order passive low pass filter 100. Here Gain is defined as 20 log(H(f)) wherein H(f)=Vout/Vin(f). The value of Gain for a passive filter in the pass band 210 is either 0 dB or slightly less than that. A cut off frequency 230 is defined such that the gain at that point is −3 dB. The power roll off 220, i.e., the slope of Gain curve 200 in the stop band beyond cutoff frequency, is −20 dB/decade. A 1st order low pass filter cannot provide a gain greater than 0 dB and a power roll off with a value more than −20 dB/decade around and beyond a cutoff frequency. In order to, achieve higher power roll off in a passive low pass filter, two such low pass filters must be cascaded to make it a second order low pass filter. Also, in order to have a gain higher than 0 dB an active filter is needed with active elements like transistors, operational amplifiers.
FIG. 2B shows an exemplar Gain vs Frequency curve 205 for a 2nd order passive low pass filter formed by cascading two first order passive low pass filters 100. The Gain is defined as 20 log(H(f)) wherein H(f)=Vout(f)/Vin(f), and the value of Gain in the pass band 215 is always 0 dB or slightly less than that. A cut off frequency 235 is defined such that the gain at that point is −3 dB. The power roll off that is the slope of Gain curve in the stop band beyond cutoff frequency 225 is −40 dB/decade. One thing to be noticed is that the power roll off has been improved significantly in the 2nd order filter. However, the gain is still 0 dB or less. In addition, the cascading 2nd order passive low pass filter requires duplication of electric components of the first order passive low pass filter.
Another type of filters is RLC filters implemented based on combinations of resistors (R), inductors (L) and capacitors (C). The RLC filters are also known as passive filters, because they do not depend upon an external power supply and/or they do not contain active components such as transistors. The RLC filters can be configured to form a resonant circuit providing a high gain for a particular band of frequencies.
Inductors block high-frequency signals and conduct low-frequency signals, while capacitors do the reverse. A filter in which the signal passes through an inductor, or in which a capacitor provides a path to ground, presents less attenuation to low-frequency signals than high-frequency signals and is therefore a low-pass filter. If the signal passes through a capacitor, or has a path to ground through an inductor, then the filter presents less attenuation to high-frequency signals than low-frequency signals and therefore is a high-pass filter. Resistors on their own have no frequency-selective properties, but are added to inductors and capacitors to determine the time-constants of the circuit, and therefore the frequencies to which it responds.
The RLC filters can provide better power roll off than the 1st order passive filter. However, inductors are very bulky due to their need to store energy in a form of current. To that end, fabricating/realizing an inductor in an integrated circuit (IC) in very difficult and consumes a lot of die area. In addition, the RLC filters also do not provide gain greater than 0 dB.
There is a pressing need to develop a compact and efficient circuit that can provide Gain in the pass band and higher roll of frequency without using any active elements, such as transistors and operational amplifier.